GCSE Maths Practice: relative-frequency

Question 9 of 11

This question asks you to use experimental data to estimate outcomes in a larger number of trials.

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\( \begin{array}{l}\text{In an experiment, a biased spinner landed on yellow} \\ \text{8 times in 25 spins. Estimate how many times it would} \\ \text{land on yellow in 100 spins.}\end{array} \)

Choose one option:

Use the observed relative frequency as an estimate and scale it to the required number of trials.

Using Relative Frequency to Predict Future Results

At Higher GCSE level, relative frequency is often used as a tool for making predictions. Rather than focusing only on what has already happened, you are asked to use experimental data to estimate what may happen if the experiment is repeated on a larger scale. This skill combines probability with proportional reasoning.

From Small Samples to Larger Experiments

In many experiments, especially in real life, data is collected from a limited number of trials. Relative frequency allows us to take this small sample and scale it up to make predictions about future outcomes. While these predictions are not exact, they provide a reasonable estimate based on the evidence available.

General Method

To estimate future outcomes using relative frequency:

  • Calculate the relative frequency from the original experiment.
  • Use this value as an estimate of probability.
  • Multiply the estimated probability by the new number of trials.
  • Interpret the result as an estimate, not a guarantee.

Worked Example 1

A spinner is spun 30 times and lands on blue 11 times. The relative frequency of blue is calculated and then multiplied by 150 to estimate how many times blue would appear in 150 spins.

Worked Example 2

A dice is rolled 50 times and lands on a six 9 times. The relative frequency of rolling a six is used to estimate how many sixes might appear if the dice is rolled 200 times.

Worked Example 3

A survey records that 18 out of 40 people prefer cycling to work. This relative frequency is scaled up to estimate how many people in a group of 500 might prefer cycling.

Why the Spinner Being Biased Matters

When a spinner or dice is described as biased, it means outcomes are not equally likely. In such cases, theoretical probability is less useful, and experimental probability becomes more important. Relative frequency reflects how the spinner actually behaves, making it the best tool for prediction.

Common Higher-Tier Mistakes

  • Using theoretical probability instead of experimental results.
  • Forgetting to multiply by the new number of trials.
  • Assuming the estimate will be exact.
  • Rounding too early during calculations.

Why Predictions Are Only Estimates

Even with a biased spinner, results can vary from one experiment to another. Random variation means that predictions based on relative frequency may not match future results exactly. However, larger numbers of trials usually make predictions more reliable.

Real-Life Uses of This Method

This approach is widely used outside school. Businesses predict future sales based on past data, scientists estimate outcomes of further experiments, and sports analysts use past performance to predict future results. In all cases, predictions are informed by observed evidence.

Frequently Asked Questions

Should I round my estimate?
Only if the question specifically asks you to.

Why not repeat the experiment instead?
Repeating experiments is ideal, but predictions are often needed before more data is available.

Does a small sample make the estimate unreliable?
Smaller samples are less reliable, but they can still give useful estimates.

Study Tip

In Higher GCSE questions, words like "estimate", "predict", or "how many times would you expect" signal that you should calculate relative frequency and scale it to the new number of trials.

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